Generally, in order to determine the resistance of an individual circuit element, such as a resistor, both the voltage across the element and the current through the element must be known. This principle is known by those having ordinary skill in the art as Ohm's law, which states that the resistance R is equal to the ratio of the voltage V over the current I(R=V/I). Unfortunately, it is not always possible or practical to know both the voltage V and the current I for every element in a given circuit.
One application for which it is not always practical to know both the voltage V and the current I for every element is a battery module. Battery modules are commonly employed when mobility and portability are required, for example, in electric automobiles, robotic systems, various types of protective suits, and the like. A typical battery module comprises a network of electrochemical cells connected, or strung, together to produce a certain amount of electric power. The exact number of cells in a given battery design depends on the amount of power required by the end equipment. These cells, or “strings,” may be connected in parallel, in series, or a combination of both (e.g., several sets of parallel strings connected in series with one another).
An example of a battery module 10 with parallel connected strings is illustrated schematically in FIG. 1A. As can be seen, the network of strings may be represented as an electrical circuit, with the branches of the circuit representing the individual strings, S1, S2, S3, and S4. Each string S1–S4 may be modeled as a constant voltage source connected in series with a resistor R1, R2, R3, and R4. The total current through the battery module 10 at any given time is I and the voltage across the battery module 10 is V. A battery module 12 with series connected strings is illustrated schematically in FIG. 1B along with the total current and voltage therefor.
It is often useful to know the resistance R1, R2, R3, or R4 in a particular string of a battery module in order to determine the health of the battery. A higher-than-expected string resistance may indicate, for example, that the battery is malfunctioning and may need to be replaced. The most direct way to determine the string resistance is to divide the voltage across the string by the current through the string (R=V/I). However, while the voltage across each string in the parallel string battery 10 is readily available, the current through each string is not. Similarly, while the current through each string in the series string battery 12 is readily available, the voltage across each string is not. To obtain the current/voltage, a current/voltage meter usually has to be deployed across each string and the current/voltage measured. Such an arrangement is not always convenient or practical, especially if the battery module is surrounded by other equipment or difficult to access. And while remote or wireless monitoring of the string voltage and current is possible, actual implementation can be overly complicated and/or costly.
Accordingly, what is needed is a way to determine individual parallel-connected string resistance in a battery module when the current through each string is unknown, and a way to determine individual series-connected string resistance when the voltage across each string is unknown.